I thought this needed sharing with MN...
I used to peel the things (mess) then slice away at the outer bit whislt trying to grasp the slippery fruit etc (more mess), and then serve it on a plate (looks like little bits of horrible mess) etc.
But a few years ago in Mexico I saw how the locals did it and it was very clever...
Hold the mango vertically, make one cut all the way through just skimming the stone. Place the cut half you've just sliced off onto a cutting board, with the flesh towards you, and make a series of cuts just shy of the skin running from top to bottom about 15mm (fat finger width) wide. Spin it around and make similar cuts the other way (again, just shy of cutting the skin). Then you grab your half mango, and kind of turn it inside out ! Ta da ! funny little squares of delicious mango are presented for one's gob and one is not covered in goo. It is quite pretty.